On projective $q^r$-divisible codes

Abstract

A projective linear code over F q is called ∆-divisible if all weights of its codewords are divisible by ∆. Especially, q r -divisible projective linear codes, where r is some integer, arise in many applications of collections of subspaces in F v q . One example are upper bounds on the cardinality of partial spreads. Here we survey the known results on the possible lengths of projective q r -divisible linear codes.